gL1 scheme for solving a class of generalized time-fractional diffusion equations
In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numer...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/160835 |
| _version_ | 1826116954995294208 |
|---|---|
| author | Li, Xuhao Wong, Patricia Jia Ying |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Li, Xuhao Wong, Patricia Jia Ying |
| author_sort | Li, Xuhao |
| collection | NTU |
| description | In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is (2 − α) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme. |
| first_indexed | 2024-10-01T04:19:52Z |
| format | Journal Article |
| id | ntu-10356/160835 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:19:52Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1608352022-08-03T06:20:26Z gL1 scheme for solving a class of generalized time-fractional diffusion equations Li, Xuhao Wong, Patricia Jia Ying School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Generalized Fractional Derivative Time-Diffusion Problem In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is (2 − α) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme. Published version 2022-08-03T06:20:26Z 2022-08-03T06:20:26Z 2022 Journal Article Li, X. & Wong, P. J. Y. (2022). gL1 scheme for solving a class of generalized time-fractional diffusion equations. Mathematics, 10(8), 1219-. https://dx.doi.org/10.3390/math10081219 2227-7390 https://hdl.handle.net/10356/160835 10.3390/math10081219 2-s2.0-85128742152 8 10 1219 en Mathematics © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Generalized Fractional Derivative Time-Diffusion Problem Li, Xuhao Wong, Patricia Jia Ying gL1 scheme for solving a class of generalized time-fractional diffusion equations |
| title | gL1 scheme for solving a class of generalized time-fractional diffusion equations |
| title_full | gL1 scheme for solving a class of generalized time-fractional diffusion equations |
| title_fullStr | gL1 scheme for solving a class of generalized time-fractional diffusion equations |
| title_full_unstemmed | gL1 scheme for solving a class of generalized time-fractional diffusion equations |
| title_short | gL1 scheme for solving a class of generalized time-fractional diffusion equations |
| title_sort | gl1 scheme for solving a class of generalized time fractional diffusion equations |
| topic | Engineering::Electrical and electronic engineering Generalized Fractional Derivative Time-Diffusion Problem |
| url | https://hdl.handle.net/10356/160835 |
| work_keys_str_mv | AT lixuhao gl1schemeforsolvingaclassofgeneralizedtimefractionaldiffusionequations AT wongpatriciajiaying gl1schemeforsolvingaclassofgeneralizedtimefractionaldiffusionequations |